Funny, I've seen this same question on three different shooting forums lately. The rising cost of components must be causing reloaders to think about having fewer components on hand.
Anyway...
For the calibers mentioned, there are several powders that will work - but not be ideal at the far ends of the cartridge spread. So load performance will suffer a bit with the largest and smallest cases.
Medium-burners such as H and IMR 4895, IMR and XMR 4064, Reloder 15, Varget, N135 or Norma 203 are all good to excellent in the .308 and .30-06 and at least fairly good in the .223 and 7 RemMag. Of the bunch, I'd gravitate to Reloder 15 because it measures extremely well, often produces the highest velocity of similar powders and is temp insensitive to boot.
I didn't list any ball powders because they can sometimes tend to get a little erratic at lower case volumes - and so they are dubious in this burn rate in the 7 Mag. But if we skip the big 7, then H335, TAC, 748, BLC2 and H380 could be considered as well. If you must have the big 7, Big Game, H414 and 760 would be good, but we'd have to eliminate the .223.
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